I can speculate a few reasons SWA excludes itself from other agencies or sites, and chooses to sell exclusively on their own website:
- It may cost money to be in those systems, either explicitly through fees or implicitly through added overhead due to commissions.
- Southwest might lose its reputation as a low-cost carrier if its fares were shown side-by-side with other carriers.
Regarding the first point, Google doesn't need the fee revenue, and including SWA in the search results will drive more traffic to SWA's own website. There is precedent. SWA lists fares both on Travelport and Expedia's Egencia. Comparison-shopping is ok for corporate travel, but not regular consumers?
Regarding the second point, in my personal experience, Southwest's fares are definitely more expensive than competitors', to the tune of about 25%. But SWA is more customer-friendly. It is much better not being hit with fees for every little thing. Flying American? Want to check a bag? Fee. Want to switch flights? Fee. Want to cancel your reservation? Fee. Want to redeem a rewards ticket without enough notice? Fee.
You pay more for Southwest's flexibility. Is it worth it? Probably.
Maybe it doesn't make sense to allow "ordinary" people to comparison shop if they lose their reputation for being cheap. If big G really wanted to list SWA prices I can imagine, say, only listing their prices on pages where you also show the competitors' fares with one checked bag included while also listing the base fare. That seems fair, pun intended.